Graph spectral domain shape representation

One of the major challenges in shape matching is recognising and interpreting the small variations in objects that are distinctly similar in their global structure, as in well known ETU10 silhouette dataset and the Tool dataset. The solution lies in modelling these variations with numerous precise details. This paper presents a novel approach based on fitting shape's local details into an adaptive spectral graph domain features. The proposed framework constructs an adaptive graph model on the boundaries of silhouette images based on threshold, in such a way that reveals small differences. This follows feature extraction on the spectral domain for shape representation. The proposed method shows that interpreting local details leading to improve the accuracy levels by 2% to 7% for the two datasets mentioned above, respectively

Point Cloud Attacks in Graph Spectral Domain: When 3D Geometry Meets Graph Signal Processing

With the increasing attention in various 3D safety-critical applications, point cloud learning models have been shown to be vulnerable to adversarial attacks. Although existing 3D attack methods achieve high success rates, they delve into the data space with point-wise perturbation, which may neglect the geometric characteristics. Instead, we propose point cloud attacks from a new perspective -- the graph spectral domain attack, aiming to perturb graph transform coefficients in the spectral domain that corresponds to varying certain geometric structure. Specifically, leveraging on graph signal processing, we first adaptively transform the coordinates of points onto the spectral domain via graph Fourier transform (GFT) for compact representation. Then, we analyze the influence of different spectral bands on the geometric structure, based on which we propose to perturb the GFT coefficients via a learnable graph spectral filter. Considering the low-frequency components mainly contribute to the rough shape of the 3D object, we further introduce a low-frequency constraint to limit perturbations within imperceptible high-frequency components. Finally, the adversarial point cloud is generated by transforming the perturbed spectral representation back to the data domain via the inverse GFT. Experimental results demonstrate the effectiveness of the proposed attack in terms of both the imperceptibility and attack success rates.Comment: Accepted to IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI). arXiv admin note: substantial text overlap with arXiv:2202.0726

Graph spectral domain features for static hand gesture recognition

The graph spectral processing is gaining increasing interest in the computer vision society because of its ability to characterize the shape. However, the graph spectral methods are usually high computational cost and one solution to simplify the problem is to automatically divide the graph into several sub-graphs. Therefore, we utilize a graph spectral domain feature representation based on the shape silhouette and we introduce a fully automatic divisive hierarchical clustering method based on the shape skeleton for static hand gesture recognition. In particular, we establish the ability of the Fiedler vector for partitioning 3D shapes. Several rules are applied to achieve a stable graph segmentation. The generated sub-graphs are used for matching purposes. Supporting results based on several datasets demonstrate the performance of the proposed method compared to the state-of-the-art methods by increment 0.3% and 3.8% for two datasets

Graph spectral domain feature learning with application to in-air hand-drawn number and shape recognition

This paper addresses the problem of recognition of dynamic shapes by representing the structure in a shape as a graph and learning the graph spectral domain features. Our proposed method includes pre-processing for converting the dynamic shapes into a fully connected graph, followed by analysis of the eigenvectors of the normalized Laplacian of the graph adjacency matrix for forming the feature vectors. The method proposes to use the eigenvector corresponding to the lowest eigenvalue for formulating the feature vectors as it captures the details of the structure of the graph. The use of the proposed graph spectral domain representation has been demonstrated in an in-air hand-drawn number and symbol recognition applications. It has achieved average accuracy rates of 99.56% and 99.44%, for numbers and symbols, respectively, outperforming the existing methods for all datasets used. It also has the added benefits of fast real-time operation and invariance to rotation and flipping, making the recognition system robust to different writing and drawing variations

Geometric deep learning: going beyond Euclidean data

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field

Geometric deep learning

The goal of these course notes is to describe the main mathematical ideas behind geometric deep learning and to provide implementation details for several applications in shape analysis and synthesis, computer vision and computer graphics. The text in the course materials is primarily based on previously published work. With these notes we gather and provide a clear picture of the key concepts and techniques that fall under the umbrella of geometric deep learning, and illustrate the applications they enable. We also aim to provide practical implementation details for the methods presented in these works, as well as suggest further readings and extensions of these ideas

Learning SO(3) Equivariant Representations with Spherical CNNs

We address the problem of 3D rotation equivariance in convolutional neural networks. 3D rotations have been a challenging nuisance in 3D classification tasks requiring higher capacity and extended data augmentation in order to tackle it. We model 3D data with multi-valued spherical functions and we propose a novel spherical convolutional network that implements exact convolutions on the sphere by realizing them in the spherical harmonic domain. Resulting filters have local symmetry and are localized by enforcing smooth spectra. We apply a novel pooling on the spectral domain and our operations are independent of the underlying spherical resolution throughout the network. We show that networks with much lower capacity and without requiring data augmentation can exhibit performance comparable to the state of the art in standard retrieval and classification benchmarks.Comment: Camera-ready. Accepted to ECCV'18 as oral presentatio